A Survey of Recent Results on Spatial Reasoning via Rough Inclusions

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Abstract

The term rough inclusion was introduced as a generic term by Polkowski and Skowron in the seminal paper that laid foundations for Rough Mereology – a paradigm for Approximate Reasoning that combines ideas of Mereology – a set theory based on the notion of a part – with ideas of Rough Set Theory and Fuzzy Set Theory; in particular, its basic predicate of rough inclusion is a rendering of the notion of being a part to a degree. Rough Mereology is an approach towards constructing reasoning schemes that take into account uncertainty of either knowledge or concepts used in reasoning. This abstract reasoning methodology is therefore a constituent of the vast field of Cognitive Technologies (styled also Artificial Intelligence).

It is well–known that mereological theories of objects have been applied in Spatial Reasoning – reasoning about uncertainty in spatial contexts. The majority of theories based on mereology and applied in reasoning about spatial objects stem from the idea of A. N. Whitehead, viz., Mereology Theory based on the predicate of being connected.

In this article, we give a survey of the current state of the art in spatial reasoning based on constructs of Rough Mereology. We include here theoretical results – some of them already shown in earlier works – that witness applicability of constructs based on rough inclusions in spatial reasoning as well as we mention recent works on practical applications to real–world robot navigation.

This article is based on the keynote lecture by the author at IMTCI (Intelligent Media Technology for Communicative Intelligence) International Workshop, Polish–Japanese Institute of Information Technology, Warsaw, September 2004.